"For those wondering, Bingham is my mum's maiden name," Bellamy explained a few days after his son's arrival "Bing Russell was also Kurt [Russell's] dad. Family connections all around!" ("Hawn" is a tribute to Hudson's mom Goldie Hawn, whose longtime partner is actor Kurt Russell.)

Bellamy (Hudson confirmed their engagement in late April on live TV) praised his love's courage during labor.

"Mum was a warrior, Bing popped out after 4.5 hours of intense pushing!"

Hudson, Bellamy and little Bingham (concealed and swaddled with a blanket) stepped out together at LAX Monday. Second-time mom has been quietly stepping out in L.A. over the past month -- hitting the beach with Bellamy and Ryder, grabbing coffee with pals and more.